You are right, PWAs (as far as their main driver states) want to be as capable as native apps. However, there is a huge distinction in that native apps start from a baseline of (almost) full system access, and PWAs must ask for permissions for anything but trivial capabilities. Permission interactions can be fine tuned on a case by case basis. If they are too spammy, they can be set to require a user event, a button in the address bar, etc. It has worked perfectly fine for android in the case of push notifications. I don't use it much, but for some webapps I do appreciate it a lot. For example twitter, I like to get a notification of some interactions, and some games notify me of scheduled events or when it's my turn.

Re: "holding the web back" 1. Not having push notifications on iOS _is_ sadly a dealbreaker when chosing between creating a native app and a webapp. 2. Android has had this feature for over a decade I think, and it works fine. 3. Apple gets a huge revenue cut from all native iOS apps, and has a general "platform image" it defends.

So there _is_ a huge contradiction, in that apple does obviously hold some key feature back, in the name of privacy, pushing users to use their preferred much more invasive platform.